At time t=0, apple 1 is dropped from a bridge onto a roadway...

At time $t=0$, apple 1 is dropped from a bridge onto a roadway beneath the bridge; somewhat later, apple 2 is thrown down from the same height. Figure $2-33$ gives the vertical positions $y$ of the apples versus $t$ during the falling, until both apples have hit the roadway. The scaling is set by $t_{s}=2.0 \mathrm{~s}$. With approximately what speed is apple 2 thrown down?

Key Concepts

Initial Velocity Determination

Determining the initial velocity of an object involves using the kinematic equations and known values of displacement, time, and acceleration. This process allows one to back-calculate the speed at which an object was thrown or released from a given height when its subsequent motion is observed or graphed.

Free Fall

Free fall refers to the motion of objects where gravity is the only force acting upon them. In free fall, objects accelerate downward at a constant rate (approximately 9.81 m/s² on Earth), and this concept underpins the analysis of vertical motion for objects dropped or thrown downward.

Projectile Motion

Projectile motion describes the movement of an object that is thrown into the air and influenced only by gravity, assuming air resistance is negligible. It combines a constant horizontal velocity with a vertical acceleration due to gravity, allowing the object's position at any point in time to be determined using kinematic equations.

Kinematic Equations

Kinematic equations provide the mathematical framework to describe the motion of objects under constant acceleration. They relate displacement, initial velocity, acceleration, and time, enabling the calculation of unknowns like the initial speed required for a given motion when other parameters, such as acceleration due to gravity and total falling time, are known.

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